Unstructured numerical intensity scales: Models, protocols and errors

A sample of 62 untrained subjects were assessed on their ability to use unstructured numerical 9-point and 30 point category scales along with an unstructured line scale, using both rank-rating and serial monadic protocols. Visual stimuli were used for convenience, the task being to rate the heights of 12 easily discriminable columns of mung beans held in transparent vertical cylinders. Such stimuli had no perceptual variance, which would otherwise have added uncontrolled variance to the subjects' performance. Two measures of performance were used for each of the 6 experimental conditions. First, mean number of 'scaling errors' made in each of the six experimental conditions was computed. In this experiment, a scaling error was defined as giving a taller column a score equal to or less than a shorter column. The lower the error count, the better the subjects' performance. The second measure was to match the subjects' rating scale pattern of scores to a 'true' pattern of scores, derived from the physical measurements of the 12 columns. For this, a 'dissimilarity score' was developed. This compared the sum of the Euclidean distances between standardized true scale ratings for each of the column's 12 true heights, with those obtained from each subject. This gave a measure of the mismatch between the subject's set of scores and the true set of scores. Both the scaling error counts and the dissimilarity measures, indicated that subjects performed significantly better using the rank-rating protocol than the serial monadic. This was because of the effects of forgetting the exact intensities of stimuli once they had been removed, removal of stimuli being a necessary part of the serial monadic protocol. Subjects were penalized when using the 9-point scales, because there were too few categories to represent the different heights of all 12 columns. This introduced the concept of 'sufficient space'. Using the rank-rating protocol, the 30-point and line scales, with no memory problems and sufficient space elicited the best performances; they were not significantly different.

Automated summary

The study found that subjects performed significantly better using the rank-rating protocol than the serial monadic protocol when evaluating their ability to use numerical scales. Penalization occurred when using 9-point scales, due to insufficient categories to represent the heights of all 12 columns, introducing the concept of 'sufficient space'.